Suppose you take a job after college that pays 50000 per yea

Suppose you take a job after college that pays $50,000 per year. If your utility function is given by u(c) = 2c, then how much utility would you receive this year if you spent $45,000 this year, and saved $5,000 for retirement? How much utility would you receive this year if you instead spent all $50,000 this year? Expressed as a percent age, how much more utility would you receive if you spent all $50,000 compared to spending $45,000?

Solution

When $45,000 is spent this year,

Utility = 2 x (45,000)^0.5 = 2 x 212.13 = 424.26

When $50,000 is spent this year,

Utility = 2 x (50,000)^0.5 = 2 x 223.61 = 447.22

Increase in utility = 447.22 - 424.26 = 22.96

Difference in % = (22.96 / 424.26) x100% = 5.41%

NOTE: It\'s assumed that \"c\" in utility function means the total amount of $ spent this year.